For illustration, let us look at the RGEs of \(\textbf {Y}_d\)  and \(\textbf {Y}_e\)  with neutrino Yukawa couplings included (cf. e.g. [1]}), which read
\(\begin{split}16\pi ^2\,\mu \frac{d}{d\mu }\textbf {Y}_d=\textbf {Y}_d\bigg \lbrace &\frac{3}{2}\textbf {Y}_d^\dagger \textbf {Y}_d -\frac{3}{2}\textbf {Y}_u^\dagger \textbf {Y}_u -\frac{1}{4}g_1^2-\frac{9}{4}g_2^2-8g_3^2\\&+\text{Tr}\left[\textbf {Y}_e^\dagger \textbf {Y}_e+\textbf {Y}_\nu ^\dagger \textbf {Y}_\nu +3\textbf {Y}_d^\dagger \textbf {Y}_d+3\textbf {Y}_u^\dagger \textbf {Y}_u\right]\bigg \rbrace ,\\16\pi ^2\,\mu \frac{d}{d\mu }\textbf {Y}_e=\textbf {Y}_e\bigg \lbrace &\frac{3}{2}\textbf {Y}_e^\dagger \textbf {Y}_e -\frac{3}{2}\textbf {Y}_\nu ^\dagger \textbf {Y}_\nu -\frac{9}{4}g_1^2-\frac{9}{4}g_2^2\\&+\text{Tr}\left[\textbf {Y}_e^\dagger \textbf {Y}_e+\textbf {Y}_\nu ^\dagger \textbf {Y}_\nu +3\textbf {Y}_d^\dagger \textbf {Y}_d+3\textbf {Y}_u^\dagger \textbf {Y}_u\right]\bigg \rbrace .\end{split}\) 
